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Simplifying -16t2 + -18t + 315 = 0 Reorder the terms: 315 + -18t + -16t2 = 0 Solving 315 + -18t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -19.6875 + 1.125t + t2 = 0 Move the constant term to the right: Add '19.6875' to each side of the equation. -19.6875 + 1.125t + 19.6875 + t2 = 0 + 19.6875 Reorder the terms: -19.6875 + 19.6875 + 1.125t + t2 = 0 + 19.6875 Combine like terms: -19.6875 + 19.6875 = 0.0000 0.0000 + 1.125t + t2 = 0 + 19.6875 1.125t + t2 = 0 + 19.6875 Combine like terms: 0 + 19.6875 = 19.6875 1.125t + t2 = 19.6875 The t term is 1.125t. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125t + 0.31640625 + t2 = 19.6875 + 0.31640625 Reorder the terms: 0.31640625 + 1.125t + t2 = 19.6875 + 0.31640625 Combine like terms: 19.6875 + 0.31640625 = 20.00390625 0.31640625 + 1.125t + t2 = 20.00390625 Factor a perfect square on the left side: (t + 0.5625)(t + 0.5625) = 20.00390625 Calculate the square root of the right side: 4.472572666 Break this problem into two subproblems by setting (t + 0.5625) equal to 4.472572666 and -4.472572666.Subproblem 1
t + 0.5625 = 4.472572666 Simplifying t + 0.5625 = 4.472572666 Reorder the terms: 0.5625 + t = 4.472572666 Solving 0.5625 + t = 4.472572666 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + t = 4.472572666 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + t = 4.472572666 + -0.5625 t = 4.472572666 + -0.5625 Combine like terms: 4.472572666 + -0.5625 = 3.910072666 t = 3.910072666 Simplifying t = 3.910072666Subproblem 2
t + 0.5625 = -4.472572666 Simplifying t + 0.5625 = -4.472572666 Reorder the terms: 0.5625 + t = -4.472572666 Solving 0.5625 + t = -4.472572666 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + t = -4.472572666 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + t = -4.472572666 + -0.5625 t = -4.472572666 + -0.5625 Combine like terms: -4.472572666 + -0.5625 = -5.035072666 t = -5.035072666 Simplifying t = -5.035072666Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.910072666, -5.035072666}
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